Search results for "Hilbert"
showing 10 items of 331 documents
Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality
2018
This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …
An Innovative Ambient Identification Method
2020
Ambient modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on appl…
Upport vector machines for nonlinear kernel ARMA system identification.
2006
Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA 2k) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based syste…
Fast fringe pattern phase demodulation using FIR Hilbert transformers
2016
This paper suggests the use of FIR Hilbert transformers to extract the phase of fringe patterns. This method is computationally faster than any known spatial method that produces wrapped phase maps. Also, the algorithm does not require any parameters to be adjusted which are dependent upon the specific fringe pattern that is being processed, or upon the particular setup of the optical fringe projection system that is being used. It is therefore particularly suitable for full algorithmic automation. The accuracy and validity of the suggested method has been tested using both computer-generated and real fringe patterns. This novel algorithm has been proposed for its advantages in terms of com…
Optimizing Kernel Ridge Regression for Remote Sensing Problems
2018
Kernel methods have been very successful in remote sensing problems because of their ability to deal with high dimensional non-linear data. However, they are computationally expensive to train when a large amount of samples are used. In this context, while the amount of available remote sensing data has constantly increased, the size of training sets in kernel methods is usually restricted to few thousand samples. In this work, we modified the kernel ridge regression (KRR) training procedure to deal with large scale datasets. In addition, the basis functions in the reproducing kernel Hilbert space are defined as parameters to be also optimized during the training process. This extends the n…
Intertwining operators between different Hilbert spaces: connection with frames
2009
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.
A novel identification procedure from ambient vibration data
2020
AbstractAmbient vibration modal identification, also known as Operational Modal Analysis, aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method b…
Automatic fringe pattern enhancement using truly adaptive period-guided bidimensional empirical mode decomposition.
2020
Fringe patterns encode the information about the result of a measurement performed via widely used optical full-field testing methods, e.g., interferometry, digital holographic microscopy, moiré techniques, structured illumination etc. Affected by the optical setup, changing environment and the sample itself fringe patterns are often corrupted with substantial noise, strong and uneven background illumination and exhibit low contrast. Fringe pattern enhancement, i.e., noise minimization and background term removal, at the pre-processing stage prior to the phase map calculation (for the measurement result decoding) is therefore essential to minimize the jeopardizing effect the mentioned error…
Tempo Induction from Music Recordings Using Ensemble Empirical Mode Decomposition Analysis
2011
Tempo and beat are among the most important features of Western music. Owing to the perceptual nature of tempo, its automatic analysis and extraction remains a difficult task for a large variety of music genres. Western music notation represents musical events using a hierarchical metrical structure distinguishing different time scales. This hierarchy is often modeled using three levels: the tatum, the tactus, and the measure. The tatum represents the shortest durational value in music that is not just an accidental phenomenon (Bilmes 1993). The tactus period is the most perceptually prominent period, and is the period at which most humans would tap their feet in time with the music (Lerdah…
Adaptive Threshold, Wavelet and Hilbert Transform for QRS Detection in Electrocardiogram Signals
2017
This paper combines Hilbert and Wavelet transforms and an adaptive threshold technique to detect the QRS complex of electrocardiogram signals. The method is performed in a window framework. First, the Wavelet transform is applied to the ECG signal to remove noise. Next, the Hilbert transform is applied to detect dominant peak points in the signal. Finally, the adaptive threshold technique is applied to detect R-peaks, Q, and S points. The performance of the algorithm is evaluated against the MIT-BIH arrhythmia database, and the numerical results indicated significant detection accuracy.